Math, Art, and Game Design, Part 2: The Game Mechanics

Brian is back with his second installment of posts on designing games. You can catch up by reading the first one here: Part 1: The Game Concept.

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Math, Art, and Game Design

A Series by Brian Powers

Part 2: The Game Mechanics

At its core, a game is a an interaction comprising a certain number of players who are trying to reach some sort of goal, so two fundamental questions to answer about your game design are:

How many players can play?

What is the goal of the game?

As far as the number of players goes, I suppose you can classify games as:

Individualistic competitive games – each player is trying to win, and there is only one winner.

Coalition competitive games – players form 2 or more teams which they compete, one team being the winner

Fully cooperative games – the players all work together to overcome some obstacle inherent in the design of the game.

I love the idea of fully cooperative games, although I haven’t played many fun cooperative games. And though I may include some aspects of coalition-building, my game is going to be strictly competitive.

With regards to the game’s goal, I’d say the most common goal is to simply get the highest score of all players. Score could be based on cash, property, or just simply abstract points. Other games are designed such that players are eliminated as the game goes on with the winner being the last remaining player. These games have an inherent drawback in that the game ceases to be fun for a player once he is out of the game. Another winning condition could be a goalpost – a race to be the first to reach some milestone (this could be a certain number of points, for example).

Different people have different qualities they look for in a good game. For some people, Monopoly is a wonderful game. However, I’d posit that these are the qualities of a good game:

Self-Balancing: If someone is in the lead the game should be harder for him. Likewise, we want opportunities for underdogs to triumph.

Choices: The game should present players with interesting and challenging decisions to make.

Fun for All: The game should be as fun for the winner(s) as it is for the loser(s).

Replay Value: Mastering the strategy should take a long time (if possible at all), so the game is fun to play over and over again.

Hopefully you agree that Monopoly has NONE of these qualities. The rich get richer in while the poor wither and die. The game is only fun for the rich, while the losers are eliminated one by one. The game is, in essence, rolling dice and buying as much property as you can afford with almost no decision-making – besides choosing whether to be the doggie or the hat. (Obviously you want to be the battleship! It has guns, duh! And if you go broke you can sell it for millions of dollars!)

Before going any further, I want to show you a page from my brainstorming for my new game. This is just to show you that although my thoughts in this article are relatively organized and coherent, brainstorming the design of a game does not have to be!

Essentially my game consists of two aspects:

Players take turns making strategic choices to receive scored rewards, and

Players modify rewards that result from strategic choices.

I’m imagining a simple game board that looks like a grid, with Red’s and Blue’s rewards represented by little markers within the grid. These colored baubles can be added, moved or removed during the game to modify rewards.

Red and Blue simultaneously but secretly choose an action each, of two that I will call “passive” and “aggressive” for simplicity’s sake. The reward for each combination of actions is then doled out accordingly. In the above scenario, let’s say both Blue and Red choose the “aggressive” action; Red will receive 3 points and Blue 2.

To extend this type of game to more than two players, I imagined what role a third player might take. What if the third player did not have control of his own fate, but instead just received a reward based on the actions of players Red and Blue. Let’s call the third player “Green” and show his rewards with little green baubles:

After Red and Blue take actions, green is rewarded with known rewards – perhaps this will influence the decisions of Red and Blue. Things are starting to get interesting!

Clearly the players should have some sort of way of alternating who gets to be Red, Blue and Green… and we should extend this to allow for more players than just three. Sure – we’ll get to that. But we also have to think about how to modify the rewards game board.

Modifying the game board could be done in one of two basic ways: with small changes or by resetting the board. Small changes consist of moving one bauble, swapping two, changing the color of one, adding or removing one, etc. For resetting the board I thought of applying some archetypal scenarios to the game. Because I think these are interesting I’ll show you the reward matrix while providing a brief description. Also, to normalize the scoring of the game, I decided that these archetypes will have rewards ranging from 0 to 4 for each player. Thus we can expect points awarded each round to be roughly in the same ballpark. The numbers in each quadrant of the grid are ordered pairs: the first is Red’s reward, and the second Blue’s reward.

Prisoner’s Dilemma

3,3

0,4

4,0

1,1

Joint passivity is highly rewarding, but each player has a temptation for aggression. However, joint aggression puts both players at a disadvantage. What a dilemma!

Stag Hunt

4,4

1,3

3,1

2,2

Both players are highly rewarded for passivity. Players are only tempted towards aggression if they suspect their opponent will do the same. This is similar to the prisoner’s dilemma but slightly different because the temptation towards aggression is not as strong.

Awkward Sidewalk

0,0

2,2

2,2

0,0

This game can be thought of as two people walking towards each other on the sidewalk. If they both stay the course then they have to stop awkwardly. If they both step to the side then it’s awkward again. Both players are only rewarded if one keeps walking while the other steps to the side.

Chicken

1,1

0,4

4,0

0,0

Two people drive their cars towards a cliff. The last person to brake wins. The actions can be thought of “brake early” and “wait for the other person to brake”. The chicken brakes early and gets nothing (just shame) while the brave one gets a big reward (fame and praise). But if both players wait for the other to brake then they both drive off the cliff, and neither gets a reward.

There are other archetypal scenarios that I’ve identified and would like to include, each with a different psychological profile and strategy set for the players. I imagine the overall structure of my game is this:

The board starts with a basic archetypal scenario, and the players modify rewards; Red and Blue choose actions, then points are scored. This is repeated twice more before the board is reset to a new game archetype. To throw Green’s baubles onto the board, we can have some way to somewhat randomly place them on the board. This could be done with a deck of cards that provide layouts of the green baubles, or it could be done randomly by rolling dice. That’s not too important to decide right now.

The game mechanics that I want to employ (and discuss just a little bit) are Limited Actions and Unpopular-Action Sweeteners.

Limited Actions

This is not an original concept really; it’s certainly been done before in many cool games such as Agricola, Puerto Rico, Citadels, and Meuterer (to name a few). Basically the players are presented with a limited set of actions and no two players are able to take the same action during a game round.

Unpopular-Action Sweeteners

A few games I’ve played employ something to this effect. If nobody takes an action during one round or turn, then the action is sweetened by placing a reward on it, to be received by the next player to choose that action. Every round that nobody takes the action another reward is placed on it. This way all actions will be attractive at different times and players have to decide at what point a non-strategic action has been sweetened enough to make it worthwhile.

I think it’s fine to employ game mechanics that have been done before. It would be extremely difficult to make a GOOD game that is original in all respects. However, I think it is important to do something novel in your game: perhaps the interaction of tried-and-true mechanics, or perhaps inventing something new. The modification of rewards is something I haven’t seen before, so I’m interested to see where this goes.

Without boring you with TOO many details of my brainstorming, I would say that I’m about ready to put together a rough prototype of the game and start testing it out in practice! So you can look forward to my next episode: The Initial Prototype. [But I want to read it now!]

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There’s a great page here that talks about different sources of tension that underlie fun decision making in games. You can see that my game relies heavily on “I think that he thinks that I think that he thinks….” But also a bit of “Build or attack”